Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2-x-7=0
-
Equation x^2+x-9=0
-
Equation -2(-2-y)-y-2=0
-
Equation x+5=13
- Express {x} in terms of y where:
- -6*x-13*y=17
- -7*x+5*y=1
- -6*x-19*y=7
- -19*x-4*y=-19
-
Identical expressions
- cos2x-sin4x= zero
- co sinus of e of 2x minus sinus of 4x equally 0
- co sinus of e of 2x minus sinus of 4x equally zero
- cos2x-sin4x=O
-
Similar expressions
- cos2x+sin4x=0
- cos(2*x)-sin(4*x)=0
cos2x-sin4x=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
cos(2*x) - sin(4*x) = 0
$$- \sin{\left(4 x \right)} + \cos{\left(2 x \right)} = 0$$
Rapid solution
[src]
-11*pi
x1 = ------
12
$$x_{1} = - \frac{11 \pi}{12}$$
-3*pi
x2 = -----
4
$$x_{2} = - \frac{3 \pi}{4}$$
-7*pi
x3 = -----
12
$$x_{3} = - \frac{7 \pi}{12}$$
-pi
x4 = ----
4
$$x_{4} = - \frac{\pi}{4}$$
pi
x5 = --
12
$$x_{5} = \frac{\pi}{12}$$
pi
x6 = --
4
$$x_{6} = \frac{\pi}{4}$$
5*pi
x7 = ----
12
$$x_{7} = \frac{5 \pi}{12}$$
3*pi
x8 = ----
4
$$x_{8} = \frac{3 \pi}{4}$$
x8 = 3*pi/4
Sum and product of roots
[src]
sum
11*pi 3*pi 7*pi pi pi pi 5*pi 3*pi
- ----- - ---- - ---- - -- + -- + -- + ---- + ----
12 4 12 4 12 4 12 4
$$\left(\left(\left(\left(\left(\left(- \frac{11 \pi}{12} - \frac{3 \pi}{4}\right) - \frac{7 \pi}{12}\right) - \frac{\pi}{4}\right) + \frac{\pi}{12}\right) + \frac{\pi}{4}\right) + \frac{5 \pi}{12}\right) + \frac{3 \pi}{4}$$
=
-pi
$$- \pi$$
product
-11*pi -3*pi -7*pi -pi pi pi 5*pi 3*pi ------*-----*-----*----*--*--*----*---- 12 4 12 4 12 4 12 4
$$\frac{3 \pi}{4} \frac{5 \pi}{12} \frac{\pi}{4} \frac{\pi}{12} \cdot - \frac{\pi}{4} \cdot - \frac{7 \pi}{12} \cdot - \frac{11 \pi}{12} \left(- \frac{3 \pi}{4}\right)$$
=
8 385*pi ------- 589824
$$\frac{385 \pi^{8}}{589824}$$
385*pi^8/589824
Numerical answer
[src]
x1 = 55.7632696012188
x2 = -33.7721210260903
x3 = 3.92699081698724
x4 = -47.9092879672443
x5 = 71.4712328691678
x6 = 46.3384916404494
x7 = -76.1836218495525
x8 = 90.3207887907066
x9 = -99.7455667514759
x10 = -65.7116463375865
x11 = -98.174770424681
x12 = -10.2101761241668
x13 = 0.261799387799149
x14 = -59.4284610304069
x15 = -89.7971900151083
x16 = -85.6083998103219
x17 = -55.7632696012188
x18 = 32.2013246992954
x19 = 18.0641577581413
x20 = 94.5095789954929
x21 = -91.8915851175014
x22 = 77.7544181763474
x23 = 22.2529479629277
x24 = 91.8915851175014
x25 = -3.92699081698724
x26 = 360.497756999429
x27 = -93.9859802198946
x28 = 40.0553063332699
x29 = -25.9181393921158
x30 = 13.8753675533549
x31 = 33.7721210260903
x32 = 2.35619449019234
x33 = 47.9092879672443
x34 = 99.7455667514759
x35 = 28.5361332701073
x36 = -11.7809724509617
x37 = -62.0464549083984
x38 = -15.4461638801498
x39 = -23.8237442897226
x40 = -18.0641577581413
x41 = -21.7293491873294
x42 = 54.1924732744239
x43 = 66.2352451131848
x44 = -71.9948316447661
x45 = 7.06858347057703
x46 = -67.8060414399797
x47 = 84.037603483527
x48 = -6.02138591938044
x49 = -77.7544181763474
x50 = 37.9609112308767
x51 = 88.2263936883134
x52 = 24.3473430653209
x53 = 15.9697626557481
x54 = 86.1319985859202
x55 = 57.857664703612
x56 = -96.0803753222878
x57 = -28.012534494509
x58 = 6.54498469497874
x59 = 85.6083998103219
x60 = -80.3724120543389
x61 = 62.0464549083984
x62 = -87.7027949127151
x63 = -30.1069295969022
x64 = 20.1585528605345
x65 = -43.720497762458
x66 = 44.2440965380563
x67 = 76.1836218495525
x68 = 69.9004365423729
x69 = 42.1497014356631
x70 = -69.9004365423729
x71 = 68.329640215578
x72 = -63.6172512351933
x73 = 98.174770424681
x74 = -74.0892267471593
x75 = -52.0980781720307
x76 = -45.8148928648512
x77 = -19.6349540849362
x78 = -8.11578102177363
x79 = -41.6261026600648
x80 = -1.83259571459405
x81 = 72.5184304203644
x82 = 64.1408500107916
x83 = -84.037603483527
x84 = 10.2101761241668
x85 = 25.9181393921158
x86 = 81.9432083811338
x87 = -37.4373124552784
x88 = 59.9520598060052
x89 = 79.8488132787406
x90 = -40.0553063332699
x91 = 11.7809724509617
x92 = 1770.02566091005
x93 = -54.1924732744239
x94 = -50.0036830696375
x95 = -32.2013246992954
x96 = 27.4889357189107
x97 = 35.8665161284835
x98 = 50.5272818452358
x98 = 50.5272818452358